Spring question please help? BEST ANSWER IN FOUR HOURS!!!?

Question

A 50.0g block is placed on a vertical spring; it compresses the spring by 10.0cm. It is then pushed down a further 20.0cm and released. What is the maximum extension of the spring if the block is attached to the spring?

How do I start this?!

Answer 1

Ok, first find the spring constant K.  You know that when the block rests on the spring, it compresses the spring 10cm.

So do a force balance...

mg = kx              

where m = mass

k = spring constant

g = 9.81 m/s^2

x = displacement

.05 kg x 9.81 m/s^2 = k x 0.1m

k = 4.905 N/m

Now, when the spring reaches its maximum extension you can assume that the block is no longer pushing down on the spring... in other words, the weight is not a factor at this state.

So now you have another force balance...initial and final

m*g + k*x1 =  k*x2

Solve for x2

where x1 is the initial displacement, and x2 is the final displacement (extension)

x2 is 40 cm